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isl_dim_replace: recursively replace parameters in nested dims
[isl.git] / isl_map_simplify.c
blobd862f9a22df3bc457e073f12671f81c6aa2a45b8
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include "isl_equalities.h"
11 #include "isl_map.h"
12 #include "isl_map_private.h"
13 #include "isl_seq.h"
14 #include "isl_tab.h"
15 #include <isl_dim_private.h>
16 #include <isl_mat_private.h>
17
18 static void swap_equality(struct isl_basic_map *bmap, int a, int b)
19 {
20 isl_int *t = bmap->eq[a];
21 bmap->eq[a] = bmap->eq[b];
22 bmap->eq[b] = t;
23 }
24
25 static void swap_inequality(struct isl_basic_map *bmap, int a, int b)
26 {
27 if (a != b) {
28 isl_int *t = bmap->ineq[a];
29 bmap->ineq[a] = bmap->ineq[b];
30 bmap->ineq[b] = t;
31 }
32 }
33
34 static void set_swap_inequality(struct isl_basic_set *bset, int a, int b)
35 {
36 swap_inequality((struct isl_basic_map *)bset, a, b);
37 }
38
39 static void constraint_drop_vars(isl_int *c, unsigned n, unsigned rem)
40 {
41 isl_seq_cpy(c, c + n, rem);
42 isl_seq_clr(c + rem, n);
43 }
44
45 /* Drop n dimensions starting at first.
46 *
47 * In principle, this frees up some extra variables as the number
48 * of columns remains constant, but we would have to extend
49 * the div array too as the number of rows in this array is assumed
50 * to be equal to extra.
51 */
52 struct isl_basic_set *isl_basic_set_drop_dims(
53 struct isl_basic_set *bset, unsigned first, unsigned n)
54 {
55 int i;
56
57 if (!bset)
58 goto error;
59
60 isl_assert(bset->ctx, first + n <= bset->dim->n_out, goto error);
61
62 if (n == 0 && !isl_dim_get_tuple_name(bset->dim, isl_dim_set))
63 return bset;
64
65 bset = isl_basic_set_cow(bset);
66 if (!bset)
67 return NULL;
68
69 for (i = 0; i < bset->n_eq; ++i)
70 constraint_drop_vars(bset->eq[i]+1+bset->dim->nparam+first, n,
71 (bset->dim->n_out-first-n)+bset->extra);
72
73 for (i = 0; i < bset->n_ineq; ++i)
74 constraint_drop_vars(bset->ineq[i]+1+bset->dim->nparam+first, n,
75 (bset->dim->n_out-first-n)+bset->extra);
76
77 for (i = 0; i < bset->n_div; ++i)
78 constraint_drop_vars(bset->div[i]+1+1+bset->dim->nparam+first, n,
79 (bset->dim->n_out-first-n)+bset->extra);
80
81 bset->dim = isl_dim_drop_outputs(bset->dim, first, n);
82 if (!bset->dim)
83 goto error;
84
85 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
86 bset = isl_basic_set_simplify(bset);
87 return isl_basic_set_finalize(bset);
88 error:
89 isl_basic_set_free(bset);
90 return NULL;
91 }
92
93 struct isl_set *isl_set_drop_dims(
94 struct isl_set *set, unsigned first, unsigned n)
95 {
96 int i;
97
98 if (!set)
99 goto error;
100
101 isl_assert(set->ctx, first + n <= set->dim->n_out, goto error);
102
103 if (n == 0 && !isl_dim_get_tuple_name(set->dim, isl_dim_set))
104 return set;
105 set = isl_set_cow(set);
106 if (!set)
107 goto error;
108 set->dim = isl_dim_drop_outputs(set->dim, first, n);
109 if (!set->dim)
110 goto error;
111
112 for (i = 0; i < set->n; ++i) {
113 set->p[i] = isl_basic_set_drop_dims(set->p[i], first, n);
114 if (!set->p[i])
115 goto error;
116 }
117
118 ISL_F_CLR(set, ISL_SET_NORMALIZED);
119 return set;
120 error:
121 isl_set_free(set);
122 return NULL;
123 }
124
125 /* Move "n" divs starting at "first" to the end of the list of divs.
126 */
127 static struct isl_basic_map *move_divs_last(struct isl_basic_map *bmap,
128 unsigned first, unsigned n)
129 {
130 isl_int **div;
131 int i;
132
133 if (first + n == bmap->n_div)
134 return bmap;
135
136 div = isl_alloc_array(bmap->ctx, isl_int *, n);
137 if (!div)
138 goto error;
139 for (i = 0; i < n; ++i)
140 div[i] = bmap->div[first + i];
141 for (i = 0; i < bmap->n_div - first - n; ++i)
142 bmap->div[first + i] = bmap->div[first + n + i];
143 for (i = 0; i < n; ++i)
144 bmap->div[bmap->n_div - n + i] = div[i];
145 free(div);
146 return bmap;
147 error:
148 isl_basic_map_free(bmap);
149 return NULL;
150 }
151
152 /* Drop "n" dimensions of type "type" starting at "first".
153 *
154 * In principle, this frees up some extra variables as the number
155 * of columns remains constant, but we would have to extend
156 * the div array too as the number of rows in this array is assumed
157 * to be equal to extra.
158 */
159 struct isl_basic_map *isl_basic_map_drop(struct isl_basic_map *bmap,
160 enum isl_dim_type type, unsigned first, unsigned n)
161 {
162 int i;
163 unsigned dim;
164 unsigned offset;
165 unsigned left;
166
167 if (!bmap)
168 goto error;
169
170 dim = isl_basic_map_dim(bmap, type);
171 isl_assert(bmap->ctx, first + n <= dim, goto error);
172
173 if (n == 0 && !isl_dim_get_tuple_name(bmap->dim, type))
174 return bmap;
175
176 bmap = isl_basic_map_cow(bmap);
177 if (!bmap)
178 return NULL;
179
180 offset = isl_basic_map_offset(bmap, type) + first;
181 left = isl_basic_map_total_dim(bmap) - (offset - 1) - n;
182 for (i = 0; i < bmap->n_eq; ++i)
183 constraint_drop_vars(bmap->eq[i]+offset, n, left);
184
185 for (i = 0; i < bmap->n_ineq; ++i)
186 constraint_drop_vars(bmap->ineq[i]+offset, n, left);
187
188 for (i = 0; i < bmap->n_div; ++i)
189 constraint_drop_vars(bmap->div[i]+1+offset, n, left);
190
191 if (type == isl_dim_div) {
192 bmap = move_divs_last(bmap, first, n);
193 if (!bmap)
194 goto error;
195 isl_basic_map_free_div(bmap, n);
196 } else
197 bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
198 if (!bmap->dim)
199 goto error;
200
201 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
202 bmap = isl_basic_map_simplify(bmap);
203 return isl_basic_map_finalize(bmap);
204 error:
205 isl_basic_map_free(bmap);
206 return NULL;
207 }
208
209 __isl_give isl_basic_set *isl_basic_set_drop(__isl_take isl_basic_set *bset,
210 enum isl_dim_type type, unsigned first, unsigned n)
211 {
212 return (isl_basic_set *)isl_basic_map_drop((isl_basic_map *)bset,
213 type, first, n);
214 }
215
216 struct isl_basic_map *isl_basic_map_drop_inputs(
217 struct isl_basic_map *bmap, unsigned first, unsigned n)
218 {
219 return isl_basic_map_drop(bmap, isl_dim_in, first, n);
220 }
221
222 struct isl_map *isl_map_drop(struct isl_map *map,
223 enum isl_dim_type type, unsigned first, unsigned n)
224 {
225 int i;
226
227 if (!map)
228 goto error;
229
230 isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
231
232 if (n == 0 && !isl_dim_get_tuple_name(map->dim, type))
233 return map;
234 map = isl_map_cow(map);
235 if (!map)
236 goto error;
237 map->dim = isl_dim_drop(map->dim, type, first, n);
238 if (!map->dim)
239 goto error;
240
241 for (i = 0; i < map->n; ++i) {
242 map->p[i] = isl_basic_map_drop(map->p[i], type, first, n);
243 if (!map->p[i])
244 goto error;
245 }
246 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
247
248 return map;
249 error:
250 isl_map_free(map);
251 return NULL;
252 }
253
254 struct isl_set *isl_set_drop(struct isl_set *set,
255 enum isl_dim_type type, unsigned first, unsigned n)
256 {
257 return (isl_set *)isl_map_drop((isl_map *)set, type, first, n);
258 }
259
260 struct isl_map *isl_map_drop_inputs(
261 struct isl_map *map, unsigned first, unsigned n)
262 {
263 return isl_map_drop(map, isl_dim_in, first, n);
264 }
265
266 /*
267 * We don't cow, as the div is assumed to be redundant.
268 */
269 static struct isl_basic_map *isl_basic_map_drop_div(
270 struct isl_basic_map *bmap, unsigned div)
271 {
272 int i;
273 unsigned pos;
274
275 if (!bmap)
276 goto error;
277
278 pos = 1 + isl_dim_total(bmap->dim) + div;
279
280 isl_assert(bmap->ctx, div < bmap->n_div, goto error);
281
282 for (i = 0; i < bmap->n_eq; ++i)
283 constraint_drop_vars(bmap->eq[i]+pos, 1, bmap->extra-div-1);
284
285 for (i = 0; i < bmap->n_ineq; ++i) {
286 if (!isl_int_is_zero(bmap->ineq[i][pos])) {
287 isl_basic_map_drop_inequality(bmap, i);
288 --i;
289 continue;
290 }
291 constraint_drop_vars(bmap->ineq[i]+pos, 1, bmap->extra-div-1);
292 }
293
294 for (i = 0; i < bmap->n_div; ++i)
295 constraint_drop_vars(bmap->div[i]+1+pos, 1, bmap->extra-div-1);
296
297 if (div != bmap->n_div - 1) {
298 int j;
299 isl_int *t = bmap->div[div];
300
301 for (j = div; j < bmap->n_div - 1; ++j)
302 bmap->div[j] = bmap->div[j+1];
303
304 bmap->div[bmap->n_div - 1] = t;
305 }
306 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
307 isl_basic_map_free_div(bmap, 1);
308
309 return bmap;
310 error:
311 isl_basic_map_free(bmap);
312 return NULL;
313 }
314
315 struct isl_basic_map *isl_basic_map_normalize_constraints(
316 struct isl_basic_map *bmap)
317 {
318 int i;
319 isl_int gcd;
320 unsigned total = isl_basic_map_total_dim(bmap);
321
322 if (!bmap)
323 return NULL;
324
325 isl_int_init(gcd);
326 for (i = bmap->n_eq - 1; i >= 0; --i) {
327 isl_seq_gcd(bmap->eq[i]+1, total, &gcd);
328 if (isl_int_is_zero(gcd)) {
329 if (!isl_int_is_zero(bmap->eq[i][0])) {
330 bmap = isl_basic_map_set_to_empty(bmap);
331 break;
332 }
333 isl_basic_map_drop_equality(bmap, i);
334 continue;
335 }
336 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
337 isl_int_gcd(gcd, gcd, bmap->eq[i][0]);
338 if (isl_int_is_one(gcd))
339 continue;
340 if (!isl_int_is_divisible_by(bmap->eq[i][0], gcd)) {
341 bmap = isl_basic_map_set_to_empty(bmap);
342 break;
343 }
344 isl_seq_scale_down(bmap->eq[i], bmap->eq[i], gcd, 1+total);
345 }
346
347 for (i = bmap->n_ineq - 1; i >= 0; --i) {
348 isl_seq_gcd(bmap->ineq[i]+1, total, &gcd);
349 if (isl_int_is_zero(gcd)) {
350 if (isl_int_is_neg(bmap->ineq[i][0])) {
351 bmap = isl_basic_map_set_to_empty(bmap);
352 break;
353 }
354 isl_basic_map_drop_inequality(bmap, i);
355 continue;
356 }
357 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
358 isl_int_gcd(gcd, gcd, bmap->ineq[i][0]);
359 if (isl_int_is_one(gcd))
360 continue;
361 isl_int_fdiv_q(bmap->ineq[i][0], bmap->ineq[i][0], gcd);
362 isl_seq_scale_down(bmap->ineq[i]+1, bmap->ineq[i]+1, gcd, total);
363 }
364 isl_int_clear(gcd);
365
366 return bmap;
367 }
368
369 struct isl_basic_set *isl_basic_set_normalize_constraints(
370 struct isl_basic_set *bset)
371 {
372 return (struct isl_basic_set *)isl_basic_map_normalize_constraints(
373 (struct isl_basic_map *)bset);
374 }
375
376 /* Assumes divs have been ordered if keep_divs is set.
377 */
378 static void eliminate_var_using_equality(struct isl_basic_map *bmap,
379 unsigned pos, isl_int *eq, int keep_divs, int *progress)
380 {
381 unsigned total;
382 int k;
383 int last_div;
384
385 total = isl_basic_map_total_dim(bmap);
386 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
387 bmap->n_div);
388 for (k = 0; k < bmap->n_eq; ++k) {
389 if (bmap->eq[k] == eq)
390 continue;
391 if (isl_int_is_zero(bmap->eq[k][1+pos]))
392 continue;
393 if (progress)
394 *progress = 1;
395 isl_seq_elim(bmap->eq[k], eq, 1+pos, 1+total, NULL);
396 }
397
398 for (k = 0; k < bmap->n_ineq; ++k) {
399 if (isl_int_is_zero(bmap->ineq[k][1+pos]))
400 continue;
401 if (progress)
402 *progress = 1;
403 isl_seq_elim(bmap->ineq[k], eq, 1+pos, 1+total, NULL);
404 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
405 }
406
407 for (k = 0; k < bmap->n_div; ++k) {
408 if (isl_int_is_zero(bmap->div[k][0]))
409 continue;
410 if (isl_int_is_zero(bmap->div[k][1+1+pos]))
411 continue;
412 if (progress)
413 *progress = 1;
414 /* We need to be careful about circular definitions,
415 * so for now we just remove the definition of div k
416 * if the equality contains any divs.
417 * If keep_divs is set, then the divs have been ordered
418 * and we can keep the definition as long as the result
419 * is still ordered.
420 */
421 if (last_div == -1 || (keep_divs && last_div < k))
422 isl_seq_elim(bmap->div[k]+1, eq,
423 1+pos, 1+total, &bmap->div[k][0]);
424 else
425 isl_seq_clr(bmap->div[k], 1 + total);
426 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
427 }
428 }
429
430 /* Assumes divs have been ordered if keep_divs is set.
431 */
432 static void eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
433 unsigned div, int keep_divs)
434 {
435 unsigned pos = isl_dim_total(bmap->dim) + div;
436
437 eliminate_var_using_equality(bmap, pos, eq, keep_divs, NULL);
438
439 isl_basic_map_drop_div(bmap, div);
440 }
441
442 /* Check if elimination of div "div" using equality "eq" would not
443 * result in a div depending on a later div.
444 */
445 static int ok_to_eliminate_div(struct isl_basic_map *bmap, isl_int *eq,
446 unsigned div)
447 {
448 int k;
449 int last_div;
450 unsigned pos = isl_dim_total(bmap->dim) + div;
451
452 last_div = isl_seq_last_non_zero(eq + 1 + isl_dim_total(bmap->dim),
453 bmap->n_div);
454 if (last_div < 0 || last_div <= div)
455 return 1;
456
457 for (k = 0; k <= last_div; ++k) {
458 if (isl_int_is_zero(bmap->div[k][0]))
459 return 1;
460 if (!isl_int_is_zero(bmap->div[k][1 + 1 + pos]))
461 return 0;
462 }
463
464 return 1;
465 }
466
467 /* Elimininate divs based on equalities
468 */
469 static struct isl_basic_map *eliminate_divs_eq(
470 struct isl_basic_map *bmap, int *progress)
471 {
472 int d;
473 int i;
474 int modified = 0;
475 unsigned off;
476
477 bmap = isl_basic_map_order_divs(bmap);
478
479 if (!bmap)
480 return NULL;
481
482 off = 1 + isl_dim_total(bmap->dim);
483
484 for (d = bmap->n_div - 1; d >= 0 ; --d) {
485 for (i = 0; i < bmap->n_eq; ++i) {
486 if (!isl_int_is_one(bmap->eq[i][off + d]) &&
487 !isl_int_is_negone(bmap->eq[i][off + d]))
488 continue;
489 if (!ok_to_eliminate_div(bmap, bmap->eq[i], d))
490 continue;
491 modified = 1;
492 *progress = 1;
493 eliminate_div(bmap, bmap->eq[i], d, 1);
494 isl_basic_map_drop_equality(bmap, i);
495 break;
496 }
497 }
498 if (modified)
499 return eliminate_divs_eq(bmap, progress);
500 return bmap;
501 }
502
503 /* Elimininate divs based on inequalities
504 */
505 static struct isl_basic_map *eliminate_divs_ineq(
506 struct isl_basic_map *bmap, int *progress)
507 {
508 int d;
509 int i;
510 unsigned off;
511 struct isl_ctx *ctx;
512
513 if (!bmap)
514 return NULL;
515
516 ctx = bmap->ctx;
517 off = 1 + isl_dim_total(bmap->dim);
518
519 for (d = bmap->n_div - 1; d >= 0 ; --d) {
520 for (i = 0; i < bmap->n_eq; ++i)
521 if (!isl_int_is_zero(bmap->eq[i][off + d]))
522 break;
523 if (i < bmap->n_eq)
524 continue;
525 for (i = 0; i < bmap->n_ineq; ++i)
526 if (isl_int_abs_gt(bmap->ineq[i][off + d], ctx->one))
527 break;
528 if (i < bmap->n_ineq)
529 continue;
530 *progress = 1;
531 bmap = isl_basic_map_eliminate_vars(bmap, (off-1)+d, 1);
532 if (!bmap || ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
533 break;
534 bmap = isl_basic_map_drop_div(bmap, d);
535 if (!bmap)
536 break;
537 }
538 return bmap;
539 }
540
541 struct isl_basic_map *isl_basic_map_gauss(
542 struct isl_basic_map *bmap, int *progress)
543 {
544 int k;
545 int done;
546 int last_var;
547 unsigned total_var;
548 unsigned total;
549
550 bmap = isl_basic_map_order_divs(bmap);
551
552 if (!bmap)
553 return NULL;
554
555 total = isl_basic_map_total_dim(bmap);
556 total_var = total - bmap->n_div;
557
558 last_var = total - 1;
559 for (done = 0; done < bmap->n_eq; ++done) {
560 for (; last_var >= 0; --last_var) {
561 for (k = done; k < bmap->n_eq; ++k)
562 if (!isl_int_is_zero(bmap->eq[k][1+last_var]))
563 break;
564 if (k < bmap->n_eq)
565 break;
566 }
567 if (last_var < 0)
568 break;
569 if (k != done)
570 swap_equality(bmap, k, done);
571 if (isl_int_is_neg(bmap->eq[done][1+last_var]))
572 isl_seq_neg(bmap->eq[done], bmap->eq[done], 1+total);
573
574 eliminate_var_using_equality(bmap, last_var, bmap->eq[done], 1,
575 progress);
576
577 if (last_var >= total_var &&
578 isl_int_is_zero(bmap->div[last_var - total_var][0])) {
579 unsigned div = last_var - total_var;
580 isl_seq_neg(bmap->div[div]+1, bmap->eq[done], 1+total);
581 isl_int_set_si(bmap->div[div][1+1+last_var], 0);
582 isl_int_set(bmap->div[div][0],
583 bmap->eq[done][1+last_var]);
584 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
585 }
586 }
587 if (done == bmap->n_eq)
588 return bmap;
589 for (k = done; k < bmap->n_eq; ++k) {
590 if (isl_int_is_zero(bmap->eq[k][0]))
591 continue;
592 return isl_basic_map_set_to_empty(bmap);
593 }
594 isl_basic_map_free_equality(bmap, bmap->n_eq-done);
595 return bmap;
596 }
597
598 struct isl_basic_set *isl_basic_set_gauss(
599 struct isl_basic_set *bset, int *progress)
600 {
601 return (struct isl_basic_set*)isl_basic_map_gauss(
602 (struct isl_basic_map *)bset, progress);
603 }
604
605
606 static unsigned int round_up(unsigned int v)
607 {
608 int old_v = v;
609
610 while (v) {
611 old_v = v;
612 v ^= v & -v;
613 }
614 return old_v << 1;
615 }
616
617 static int hash_index(isl_int ***index, unsigned int size, int bits,
618 struct isl_basic_map *bmap, int k)
619 {
620 int h;
621 unsigned total = isl_basic_map_total_dim(bmap);
622 uint32_t hash = isl_seq_get_hash_bits(bmap->ineq[k]+1, total, bits);
623 for (h = hash; index[h]; h = (h+1) % size)
624 if (&bmap->ineq[k] != index[h] &&
625 isl_seq_eq(bmap->ineq[k]+1, index[h][0]+1, total))
626 break;
627 return h;
628 }
629
630 static int set_hash_index(isl_int ***index, unsigned int size, int bits,
631 struct isl_basic_set *bset, int k)
632 {
633 return hash_index(index, size, bits, (struct isl_basic_map *)bset, k);
634 }
635
636 /* If we can eliminate more than one div, then we need to make
637 * sure we do it from last div to first div, in order not to
638 * change the position of the other divs that still need to
639 * be removed.
640 */
641 static struct isl_basic_map *remove_duplicate_divs(
642 struct isl_basic_map *bmap, int *progress)
643 {
644 unsigned int size;
645 int *index;
646 int *elim_for;
647 int k, l, h;
648 int bits;
649 struct isl_blk eq;
650 unsigned total_var;
651 unsigned total;
652 struct isl_ctx *ctx;
653
654 if (!bmap || bmap->n_div <= 1)
655 return bmap;
656
657 total_var = isl_dim_total(bmap->dim);
658 total = total_var + bmap->n_div;
659
660 ctx = bmap->ctx;
661 for (k = bmap->n_div - 1; k >= 0; --k)
662 if (!isl_int_is_zero(bmap->div[k][0]))
663 break;
664 if (k <= 0)
665 return bmap;
666
667 elim_for = isl_calloc_array(ctx, int, bmap->n_div);
668 size = round_up(4 * bmap->n_div / 3 - 1);
669 bits = ffs(size) - 1;
670 index = isl_calloc_array(ctx, int, size);
671 if (!index)
672 return bmap;
673 eq = isl_blk_alloc(ctx, 1+total);
674 if (isl_blk_is_error(eq))
675 goto out;
676
677 isl_seq_clr(eq.data, 1+total);
678 index[isl_seq_get_hash_bits(bmap->div[k], 2+total, bits)] = k + 1;
679 for (--k; k >= 0; --k) {
680 uint32_t hash;
681
682 if (isl_int_is_zero(bmap->div[k][0]))
683 continue;
684
685 hash = isl_seq_get_hash_bits(bmap->div[k], 2+total, bits);
686 for (h = hash; index[h]; h = (h+1) % size)
687 if (isl_seq_eq(bmap->div[k],
688 bmap->div[index[h]-1], 2+total))
689 break;
690 if (index[h]) {
691 *progress = 1;
692 l = index[h] - 1;
693 elim_for[l] = k + 1;
694 }
695 index[h] = k+1;
696 }
697 for (l = bmap->n_div - 1; l >= 0; --l) {
698 if (!elim_for[l])
699 continue;
700 k = elim_for[l] - 1;
701 isl_int_set_si(eq.data[1+total_var+k], -1);
702 isl_int_set_si(eq.data[1+total_var+l], 1);
703 eliminate_div(bmap, eq.data, l, 0);
704 isl_int_set_si(eq.data[1+total_var+k], 0);
705 isl_int_set_si(eq.data[1+total_var+l], 0);
706 }
707
708 isl_blk_free(ctx, eq);
709 out:
710 free(index);
711 free(elim_for);
712 return bmap;
713 }
714
715 static int n_pure_div_eq(struct isl_basic_map *bmap)
716 {
717 int i, j;
718 unsigned total;
719
720 total = isl_dim_total(bmap->dim);
721 for (i = 0, j = bmap->n_div-1; i < bmap->n_eq; ++i) {
722 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
723 --j;
724 if (j < 0)
725 break;
726 if (isl_seq_first_non_zero(bmap->eq[i] + 1 + total, j) != -1)
727 return 0;
728 }
729 return i;
730 }
731
732 /* Normalize divs that appear in equalities.
733 *
734 * In particular, we assume that bmap contains some equalities
735 * of the form
736 *
737 * a x = m * e_i
738 *
739 * and we want to replace the set of e_i by a minimal set and
740 * such that the new e_i have a canonical representation in terms
741 * of the vector x.
742 * If any of the equalities involves more than one divs, then
743 * we currently simply bail out.
744 *
745 * Let us first additionally assume that all equalities involve
746 * a div. The equalities then express modulo constraints on the
747 * remaining variables and we can use "parameter compression"
748 * to find a minimal set of constraints. The result is a transformation
749 *
750 * x = T(x') = x_0 + G x'
751 *
752 * with G a lower-triangular matrix with all elements below the diagonal
753 * non-negative and smaller than the diagonal element on the same row.
754 * We first normalize x_0 by making the same property hold in the affine
755 * T matrix.
756 * The rows i of G with a 1 on the diagonal do not impose any modulo
757 * constraint and simply express x_i = x'_i.
758 * For each of the remaining rows i, we introduce a div and a corresponding
759 * equality. In particular
760 *
761 * g_ii e_j = x_i - g_i(x')
762 *
763 * where each x'_k is replaced either by x_k (if g_kk = 1) or the
764 * corresponding div (if g_kk != 1).
765 *
766 * If there are any equalities not involving any div, then we
767 * first apply a variable compression on the variables x:
768 *
769 * x = C x'' x'' = C_2 x
770 *
771 * and perform the above parameter compression on A C instead of on A.
772 * The resulting compression is then of the form
773 *
774 * x'' = T(x') = x_0 + G x'
775 *
776 * and in constructing the new divs and the corresponding equalities,
777 * we have to replace each x'', i.e., the x'_k with (g_kk = 1),
778 * by the corresponding row from C_2.
779 */
780 static struct isl_basic_map *normalize_divs(
781 struct isl_basic_map *bmap, int *progress)
782 {
783 int i, j, k;
784 int total;
785 int div_eq;
786 struct isl_mat *B;
787 struct isl_vec *d;
788 struct isl_mat *T = NULL;
789 struct isl_mat *C = NULL;
790 struct isl_mat *C2 = NULL;
791 isl_int v;
792 int *pos;
793 int dropped, needed;
794
795 if (!bmap)
796 return NULL;
797
798 if (bmap->n_div == 0)
799 return bmap;
800
801 if (bmap->n_eq == 0)
802 return bmap;
803
804 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS))
805 return bmap;
806
807 total = isl_dim_total(bmap->dim);
808 div_eq = n_pure_div_eq(bmap);
809 if (div_eq == 0)
810 return bmap;
811
812 if (div_eq < bmap->n_eq) {
813 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, div_eq,
814 bmap->n_eq - div_eq, 0, 1 + total);
815 C = isl_mat_variable_compression(B, &C2);
816 if (!C || !C2)
817 goto error;
818 if (C->n_col == 0) {
819 bmap = isl_basic_map_set_to_empty(bmap);
820 isl_mat_free(C);
821 isl_mat_free(C2);
822 goto done;
823 }
824 }
825
826 d = isl_vec_alloc(bmap->ctx, div_eq);
827 if (!d)
828 goto error;
829 for (i = 0, j = bmap->n_div-1; i < div_eq; ++i) {
830 while (j >= 0 && isl_int_is_zero(bmap->eq[i][1 + total + j]))
831 --j;
832 isl_int_set(d->block.data[i], bmap->eq[i][1 + total + j]);
833 }
834 B = isl_mat_sub_alloc(bmap->ctx, bmap->eq, 0, div_eq, 0, 1 + total);
835
836 if (C) {
837 B = isl_mat_product(B, C);
838 C = NULL;
839 }
840
841 T = isl_mat_parameter_compression(B, d);
842 if (!T)
843 goto error;
844 if (T->n_col == 0) {
845 bmap = isl_basic_map_set_to_empty(bmap);
846 isl_mat_free(C2);
847 isl_mat_free(T);
848 goto done;
849 }
850 isl_int_init(v);
851 for (i = 0; i < T->n_row - 1; ++i) {
852 isl_int_fdiv_q(v, T->row[1 + i][0], T->row[1 + i][1 + i]);
853 if (isl_int_is_zero(v))
854 continue;
855 isl_mat_col_submul(T, 0, v, 1 + i);
856 }
857 isl_int_clear(v);
858 pos = isl_alloc_array(bmap->ctx, int, T->n_row);
859 if (!pos)
860 goto error;
861 /* We have to be careful because dropping equalities may reorder them */
862 dropped = 0;
863 for (j = bmap->n_div - 1; j >= 0; --j) {
864 for (i = 0; i < bmap->n_eq; ++i)
865 if (!isl_int_is_zero(bmap->eq[i][1 + total + j]))
866 break;
867 if (i < bmap->n_eq) {
868 bmap = isl_basic_map_drop_div(bmap, j);
869 isl_basic_map_drop_equality(bmap, i);
870 ++dropped;
871 }
872 }
873 pos[0] = 0;
874 needed = 0;
875 for (i = 1; i < T->n_row; ++i) {
876 if (isl_int_is_one(T->row[i][i]))
877 pos[i] = i;
878 else
879 needed++;
880 }
881 if (needed > dropped) {
882 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
883 needed, needed, 0);
884 if (!bmap)
885 goto error;
886 }
887 for (i = 1; i < T->n_row; ++i) {
888 if (isl_int_is_one(T->row[i][i]))
889 continue;
890 k = isl_basic_map_alloc_div(bmap);
891 pos[i] = 1 + total + k;
892 isl_seq_clr(bmap->div[k] + 1, 1 + total + bmap->n_div);
893 isl_int_set(bmap->div[k][0], T->row[i][i]);
894 if (C2)
895 isl_seq_cpy(bmap->div[k] + 1, C2->row[i], 1 + total);
896 else
897 isl_int_set_si(bmap->div[k][1 + i], 1);
898 for (j = 0; j < i; ++j) {
899 if (isl_int_is_zero(T->row[i][j]))
900 continue;
901 if (pos[j] < T->n_row && C2)
902 isl_seq_submul(bmap->div[k] + 1, T->row[i][j],
903 C2->row[pos[j]], 1 + total);
904 else
905 isl_int_neg(bmap->div[k][1 + pos[j]],
906 T->row[i][j]);
907 }
908 j = isl_basic_map_alloc_equality(bmap);
909 isl_seq_neg(bmap->eq[j], bmap->div[k]+1, 1+total+bmap->n_div);
910 isl_int_set(bmap->eq[j][pos[i]], bmap->div[k][0]);
911 }
912 free(pos);
913 isl_mat_free(C2);
914 isl_mat_free(T);
915
916 if (progress)
917 *progress = 1;
918 done:
919 ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
920
921 return bmap;
922 error:
923 isl_mat_free(C);
924 isl_mat_free(C2);
925 isl_mat_free(T);
926 return bmap;
927 }
928
929 static struct isl_basic_map *set_div_from_lower_bound(
930 struct isl_basic_map *bmap, int div, int ineq)
931 {
932 unsigned total = 1 + isl_dim_total(bmap->dim);
933
934 isl_seq_neg(bmap->div[div] + 1, bmap->ineq[ineq], total + bmap->n_div);
935 isl_int_set(bmap->div[div][0], bmap->ineq[ineq][total + div]);
936 isl_int_add(bmap->div[div][1], bmap->div[div][1], bmap->div[div][0]);
937 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
938 isl_int_set_si(bmap->div[div][1 + total + div], 0);
939
940 return bmap;
941 }
942
943 /* Check whether it is ok to define a div based on an inequality.
944 * To avoid the introduction of circular definitions of divs, we
945 * do not allow such a definition if the resulting expression would refer to
946 * any other undefined divs or if any known div is defined in
947 * terms of the unknown div.
948 */
949 static int ok_to_set_div_from_bound(struct isl_basic_map *bmap,
950 int div, int ineq)
951 {
952 int j;
953 unsigned total = 1 + isl_dim_total(bmap->dim);
954
955 /* Not defined in terms of unknown divs */
956 for (j = 0; j < bmap->n_div; ++j) {
957 if (div == j)
958 continue;
959 if (isl_int_is_zero(bmap->ineq[ineq][total + j]))
960 continue;
961 if (isl_int_is_zero(bmap->div[j][0]))
962 return 0;
963 }
964
965 /* No other div defined in terms of this one => avoid loops */
966 for (j = 0; j < bmap->n_div; ++j) {
967 if (div == j)
968 continue;
969 if (isl_int_is_zero(bmap->div[j][0]))
970 continue;
971 if (!isl_int_is_zero(bmap->div[j][1 + total + div]))
972 return 0;
973 }
974
975 return 1;
976 }
977
978 /* Given two constraints "k" and "l" that are opposite to each other,
979 * except for the constant term, check if we can use them
980 * to obtain an expression for one of the hitherto unknown divs.
981 * "sum" is the sum of the constant terms of the constraints.
982 * If this sum is strictly smaller than the coefficient of one
983 * of the divs, then this pair can be used define the div.
984 * To avoid the introduction of circular definitions of divs, we
985 * do not use the pair if the resulting expression would refer to
986 * any other undefined divs or if any known div is defined in
987 * terms of the unknown div.
988 */
989 static struct isl_basic_map *check_for_div_constraints(
990 struct isl_basic_map *bmap, int k, int l, isl_int sum, int *progress)
991 {
992 int i;
993 unsigned total = 1 + isl_dim_total(bmap->dim);
994
995 for (i = 0; i < bmap->n_div; ++i) {
996 if (!isl_int_is_zero(bmap->div[i][0]))
997 continue;
998 if (isl_int_is_zero(bmap->ineq[k][total + i]))
999 continue;
1000 if (isl_int_abs_ge(sum, bmap->ineq[k][total + i]))
1001 continue;
1002 if (!ok_to_set_div_from_bound(bmap, i, k))
1003 break;
1004 if (isl_int_is_pos(bmap->ineq[k][total + i]))
1005 bmap = set_div_from_lower_bound(bmap, i, k);
1006 else
1007 bmap = set_div_from_lower_bound(bmap, i, l);
1008 if (progress)
1009 *progress = 1;
1010 break;
1011 }
1012 return bmap;
1013 }
1014
1015 static struct isl_basic_map *remove_duplicate_constraints(
1016 struct isl_basic_map *bmap, int *progress)
1017 {
1018 unsigned int size;
1019 isl_int ***index;
1020 int k, l, h;
1021 int bits;
1022 unsigned total = isl_basic_map_total_dim(bmap);
1023 isl_int sum;
1024
1025 if (!bmap || bmap->n_ineq <= 1)
1026 return bmap;
1027
1028 size = round_up(4 * (bmap->n_ineq+1) / 3 - 1);
1029 bits = ffs(size) - 1;
1030 index = isl_calloc_array(ctx, isl_int **, size);
1031 if (!index)
1032 return bmap;
1033
1034 index[isl_seq_get_hash_bits(bmap->ineq[0]+1, total, bits)] = &bmap->ineq[0];
1035 for (k = 1; k < bmap->n_ineq; ++k) {
1036 h = hash_index(index, size, bits, bmap, k);
1037 if (!index[h]) {
1038 index[h] = &bmap->ineq[k];
1039 continue;
1040 }
1041 if (progress)
1042 *progress = 1;
1043 l = index[h] - &bmap->ineq[0];
1044 if (isl_int_lt(bmap->ineq[k][0], bmap->ineq[l][0]))
1045 swap_inequality(bmap, k, l);
1046 isl_basic_map_drop_inequality(bmap, k);
1047 --k;
1048 }
1049 isl_int_init(sum);
1050 for (k = 0; k < bmap->n_ineq-1; ++k) {
1051 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1052 h = hash_index(index, size, bits, bmap, k);
1053 isl_seq_neg(bmap->ineq[k]+1, bmap->ineq[k]+1, total);
1054 if (!index[h])
1055 continue;
1056 l = index[h] - &bmap->ineq[0];
1057 isl_int_add(sum, bmap->ineq[k][0], bmap->ineq[l][0]);
1058 if (isl_int_is_pos(sum)) {
1059 bmap = check_for_div_constraints(bmap, k, l, sum,
1060 progress);
1061 continue;
1062 }
1063 if (isl_int_is_zero(sum)) {
1064 /* We need to break out of the loop after these
1065 * changes since the contents of the hash
1066 * will no longer be valid.
1067 * Plus, we probably we want to regauss first.
1068 */
1069 if (progress)
1070 *progress = 1;
1071 isl_basic_map_drop_inequality(bmap, l);
1072 isl_basic_map_inequality_to_equality(bmap, k);
1073 } else
1074 bmap = isl_basic_map_set_to_empty(bmap);
1075 break;
1076 }
1077 isl_int_clear(sum);
1078
1079 free(index);
1080 return bmap;
1081 }
1082
1083
1084 struct isl_basic_map *isl_basic_map_simplify(struct isl_basic_map *bmap)
1085 {
1086 int progress = 1;
1087 if (!bmap)
1088 return NULL;
1089 while (progress) {
1090 progress = 0;
1091 bmap = isl_basic_map_normalize_constraints(bmap);
1092 bmap = remove_duplicate_divs(bmap, &progress);
1093 bmap = eliminate_divs_eq(bmap, &progress);
1094 bmap = eliminate_divs_ineq(bmap, &progress);
1095 bmap = isl_basic_map_gauss(bmap, &progress);
1096 /* requires equalities in normal form */
1097 bmap = normalize_divs(bmap, &progress);
1098 bmap = remove_duplicate_constraints(bmap, &progress);
1099 }
1100 return bmap;
1101 }
1102
1103 struct isl_basic_set *isl_basic_set_simplify(struct isl_basic_set *bset)
1104 {
1105 return (struct isl_basic_set *)
1106 isl_basic_map_simplify((struct isl_basic_map *)bset);
1107 }
1108
1109
1110 int isl_basic_map_is_div_constraint(__isl_keep isl_basic_map *bmap,
1111 isl_int *constraint, unsigned div)
1112 {
1113 unsigned pos;
1114
1115 if (!bmap)
1116 return -1;
1117
1118 pos = 1 + isl_dim_total(bmap->dim) + div;
1119
1120 if (isl_int_eq(constraint[pos], bmap->div[div][0])) {
1121 int neg;
1122 isl_int_sub(bmap->div[div][1],
1123 bmap->div[div][1], bmap->div[div][0]);
1124 isl_int_add_ui(bmap->div[div][1], bmap->div[div][1], 1);
1125 neg = isl_seq_is_neg(constraint, bmap->div[div]+1, pos);
1126 isl_int_sub_ui(bmap->div[div][1], bmap->div[div][1], 1);
1127 isl_int_add(bmap->div[div][1],
1128 bmap->div[div][1], bmap->div[div][0]);
1129 if (!neg)
1130 return 0;
1131 if (isl_seq_first_non_zero(constraint+pos+1,
1132 bmap->n_div-div-1) != -1)
1133 return 0;
1134 } else if (isl_int_abs_eq(constraint[pos], bmap->div[div][0])) {
1135 if (!isl_seq_eq(constraint, bmap->div[div]+1, pos))
1136 return 0;
1137 if (isl_seq_first_non_zero(constraint+pos+1,
1138 bmap->n_div-div-1) != -1)
1139 return 0;
1140 } else
1141 return 0;
1142
1143 return 1;
1144 }
1145
1146
1147 /* If the only constraints a div d=floor(f/m)
1148 * appears in are its two defining constraints
1149 *
1150 * f - m d >=0
1151 * -(f - (m - 1)) + m d >= 0
1152 *
1153 * then it can safely be removed.
1154 */
1155 static int div_is_redundant(struct isl_basic_map *bmap, int div)
1156 {
1157 int i;
1158 unsigned pos = 1 + isl_dim_total(bmap->dim) + div;
1159
1160 for (i = 0; i < bmap->n_eq; ++i)
1161 if (!isl_int_is_zero(bmap->eq[i][pos]))
1162 return 0;
1163
1164 for (i = 0; i < bmap->n_ineq; ++i) {
1165 if (isl_int_is_zero(bmap->ineq[i][pos]))
1166 continue;
1167 if (!isl_basic_map_is_div_constraint(bmap, bmap->ineq[i], div))
1168 return 0;
1169 }
1170
1171 for (i = 0; i < bmap->n_div; ++i)
1172 if (!isl_int_is_zero(bmap->div[i][1+pos]))
1173 return 0;
1174
1175 return 1;
1176 }
1177
1178 /*
1179 * Remove divs that don't occur in any of the constraints or other divs.
1180 * These can arise when dropping some of the variables in a quast
1181 * returned by piplib.
1182 */
1183 static struct isl_basic_map *remove_redundant_divs(struct isl_basic_map *bmap)
1184 {
1185 int i;
1186
1187 if (!bmap)
1188 return NULL;
1189
1190 for (i = bmap->n_div-1; i >= 0; --i) {
1191 if (!div_is_redundant(bmap, i))
1192 continue;
1193 bmap = isl_basic_map_drop_div(bmap, i);
1194 }
1195 return bmap;
1196 }
1197
1198 struct isl_basic_map *isl_basic_map_finalize(struct isl_basic_map *bmap)
1199 {
1200 bmap = remove_redundant_divs(bmap);
1201 if (!bmap)
1202 return NULL;
1203 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
1204 return bmap;
1205 }
1206
1207 struct isl_basic_set *isl_basic_set_finalize(struct isl_basic_set *bset)
1208 {
1209 return (struct isl_basic_set *)
1210 isl_basic_map_finalize((struct isl_basic_map *)bset);
1211 }
1212
1213 struct isl_set *isl_set_finalize(struct isl_set *set)
1214 {
1215 int i;
1216
1217 if (!set)
1218 return NULL;
1219 for (i = 0; i < set->n; ++i) {
1220 set->p[i] = isl_basic_set_finalize(set->p[i]);
1221 if (!set->p[i])
1222 goto error;
1223 }
1224 return set;
1225 error:
1226 isl_set_free(set);
1227 return NULL;
1228 }
1229
1230 struct isl_map *isl_map_finalize(struct isl_map *map)
1231 {
1232 int i;
1233
1234 if (!map)
1235 return NULL;
1236 for (i = 0; i < map->n; ++i) {
1237 map->p[i] = isl_basic_map_finalize(map->p[i]);
1238 if (!map->p[i])
1239 goto error;
1240 }
1241 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1242 return map;
1243 error:
1244 isl_map_free(map);
1245 return NULL;
1246 }
1247
1248
1249 /* Remove definition of any div that is defined in terms of the given variable.
1250 * The div itself is not removed. Functions such as
1251 * eliminate_divs_ineq depend on the other divs remaining in place.
1252 */
1253 static struct isl_basic_map *remove_dependent_vars(struct isl_basic_map *bmap,
1254 int pos)
1255 {
1256 int i;
1257
1258 for (i = 0; i < bmap->n_div; ++i) {
1259 if (isl_int_is_zero(bmap->div[i][0]))
1260 continue;
1261 if (isl_int_is_zero(bmap->div[i][1+1+pos]))
1262 continue;
1263 isl_int_set_si(bmap->div[i][0], 0);
1264 }
1265 return bmap;
1266 }
1267
1268 /* Eliminate the specified variables from the constraints using
1269 * Fourier-Motzkin. The variables themselves are not removed.
1270 */
1271 struct isl_basic_map *isl_basic_map_eliminate_vars(
1272 struct isl_basic_map *bmap, unsigned pos, unsigned n)
1273 {
1274 int d;
1275 int i, j, k;
1276 unsigned total;
1277
1278 if (n == 0)
1279 return bmap;
1280 if (!bmap)
1281 return NULL;
1282 total = isl_basic_map_total_dim(bmap);
1283
1284 bmap = isl_basic_map_cow(bmap);
1285 for (d = pos + n - 1; d >= 0 && d >= pos; --d)
1286 bmap = remove_dependent_vars(bmap, d);
1287
1288 for (d = pos + n - 1;
1289 d >= 0 && d >= total - bmap->n_div && d >= pos; --d)
1290 isl_seq_clr(bmap->div[d-(total-bmap->n_div)], 2+total);
1291 for (d = pos + n - 1; d >= 0 && d >= pos; --d) {
1292 int n_lower, n_upper;
1293 if (!bmap)
1294 return NULL;
1295 for (i = 0; i < bmap->n_eq; ++i) {
1296 if (isl_int_is_zero(bmap->eq[i][1+d]))
1297 continue;
1298 eliminate_var_using_equality(bmap, d, bmap->eq[i], 0, NULL);
1299 isl_basic_map_drop_equality(bmap, i);
1300 break;
1301 }
1302 if (i < bmap->n_eq)
1303 continue;
1304 n_lower = 0;
1305 n_upper = 0;
1306 for (i = 0; i < bmap->n_ineq; ++i) {
1307 if (isl_int_is_pos(bmap->ineq[i][1+d]))
1308 n_lower++;
1309 else if (isl_int_is_neg(bmap->ineq[i][1+d]))
1310 n_upper++;
1311 }
1312 bmap = isl_basic_map_extend_constraints(bmap,
1313 0, n_lower * n_upper);
1314 if (!bmap)
1315 goto error;
1316 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1317 int last;
1318 if (isl_int_is_zero(bmap->ineq[i][1+d]))
1319 continue;
1320 last = -1;
1321 for (j = 0; j < i; ++j) {
1322 if (isl_int_is_zero(bmap->ineq[j][1+d]))
1323 continue;
1324 last = j;
1325 if (isl_int_sgn(bmap->ineq[i][1+d]) ==
1326 isl_int_sgn(bmap->ineq[j][1+d]))
1327 continue;
1328 k = isl_basic_map_alloc_inequality(bmap);
1329 if (k < 0)
1330 goto error;
1331 isl_seq_cpy(bmap->ineq[k], bmap->ineq[i],
1332 1+total);
1333 isl_seq_elim(bmap->ineq[k], bmap->ineq[j],
1334 1+d, 1+total, NULL);
1335 }
1336 isl_basic_map_drop_inequality(bmap, i);
1337 i = last + 1;
1338 }
1339 if (n_lower > 0 && n_upper > 0) {
1340 bmap = isl_basic_map_normalize_constraints(bmap);
1341 bmap = remove_duplicate_constraints(bmap, NULL);
1342 bmap = isl_basic_map_gauss(bmap, NULL);
1343 bmap = isl_basic_map_remove_redundancies(bmap);
1344 if (!bmap)
1345 goto error;
1346 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1347 break;
1348 }
1349 }
1350 ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
1351 return bmap;
1352 error:
1353 isl_basic_map_free(bmap);
1354 return NULL;
1355 }
1356
1357 struct isl_basic_set *isl_basic_set_eliminate_vars(
1358 struct isl_basic_set *bset, unsigned pos, unsigned n)
1359 {
1360 return (struct isl_basic_set *)isl_basic_map_eliminate_vars(
1361 (struct isl_basic_map *)bset, pos, n);
1362 }
1363
1364 /* Don't assume equalities are in order, because align_divs
1365 * may have changed the order of the divs.
1366 */
1367 static void compute_elimination_index(struct isl_basic_map *bmap, int *elim)
1368 {
1369 int d, i;
1370 unsigned total;
1371
1372 total = isl_dim_total(bmap->dim);
1373 for (d = 0; d < total; ++d)
1374 elim[d] = -1;
1375 for (i = 0; i < bmap->n_eq; ++i) {
1376 for (d = total - 1; d >= 0; --d) {
1377 if (isl_int_is_zero(bmap->eq[i][1+d]))
1378 continue;
1379 elim[d] = i;
1380 break;
1381 }
1382 }
1383 }
1384
1385 static void set_compute_elimination_index(struct isl_basic_set *bset, int *elim)
1386 {
1387 compute_elimination_index((struct isl_basic_map *)bset, elim);
1388 }
1389
1390 static int reduced_using_equalities(isl_int *dst, isl_int *src,
1391 struct isl_basic_map *bmap, int *elim)
1392 {
1393 int d;
1394 int copied = 0;
1395 unsigned total;
1396
1397 total = isl_dim_total(bmap->dim);
1398 for (d = total - 1; d >= 0; --d) {
1399 if (isl_int_is_zero(src[1+d]))
1400 continue;
1401 if (elim[d] == -1)
1402 continue;
1403 if (!copied) {
1404 isl_seq_cpy(dst, src, 1 + total);
1405 copied = 1;
1406 }
1407 isl_seq_elim(dst, bmap->eq[elim[d]], 1 + d, 1 + total, NULL);
1408 }
1409 return copied;
1410 }
1411
1412 static int set_reduced_using_equalities(isl_int *dst, isl_int *src,
1413 struct isl_basic_set *bset, int *elim)
1414 {
1415 return reduced_using_equalities(dst, src,
1416 (struct isl_basic_map *)bset, elim);
1417 }
1418
1419 static struct isl_basic_set *isl_basic_set_reduce_using_equalities(
1420 struct isl_basic_set *bset, struct isl_basic_set *context)
1421 {
1422 int i;
1423 int *elim;
1424
1425 if (!bset || !context)
1426 goto error;
1427
1428 if (context->n_eq == 0) {
1429 isl_basic_set_free(context);
1430 return bset;
1431 }
1432
1433 bset = isl_basic_set_cow(bset);
1434 if (!bset)
1435 goto error;
1436
1437 elim = isl_alloc_array(bset->ctx, int, isl_basic_set_n_dim(bset));
1438 if (!elim)
1439 goto error;
1440 set_compute_elimination_index(context, elim);
1441 for (i = 0; i < bset->n_eq; ++i)
1442 set_reduced_using_equalities(bset->eq[i], bset->eq[i],
1443 context, elim);
1444 for (i = 0; i < bset->n_ineq; ++i)
1445 set_reduced_using_equalities(bset->ineq[i], bset->ineq[i],
1446 context, elim);
1447 isl_basic_set_free(context);
1448 free(elim);
1449 bset = isl_basic_set_simplify(bset);
1450 bset = isl_basic_set_finalize(bset);
1451 return bset;
1452 error:
1453 isl_basic_set_free(bset);
1454 isl_basic_set_free(context);
1455 return NULL;
1456 }
1457
1458 static struct isl_basic_set *remove_shifted_constraints(
1459 struct isl_basic_set *bset, struct isl_basic_set *context)
1460 {
1461 unsigned int size;
1462 isl_int ***index;
1463 int bits;
1464 int k, h, l;
1465
1466 if (!bset)
1467 return NULL;
1468
1469 size = round_up(4 * (context->n_ineq+1) / 3 - 1);
1470 bits = ffs(size) - 1;
1471 index = isl_calloc_array(ctx, isl_int **, size);
1472 if (!index)
1473 return bset;
1474
1475 for (k = 0; k < context->n_ineq; ++k) {
1476 h = set_hash_index(index, size, bits, context, k);
1477 index[h] = &context->ineq[k];
1478 }
1479 for (k = 0; k < bset->n_ineq; ++k) {
1480 h = set_hash_index(index, size, bits, bset, k);
1481 if (!index[h])
1482 continue;
1483 l = index[h] - &context->ineq[0];
1484 if (isl_int_lt(bset->ineq[k][0], context->ineq[l][0]))
1485 continue;
1486 bset = isl_basic_set_cow(bset);
1487 if (!bset)
1488 goto error;
1489 isl_basic_set_drop_inequality(bset, k);
1490 --k;
1491 }
1492 free(index);
1493 return bset;
1494 error:
1495 free(index);
1496 return bset;
1497 }
1498
1499 /* Tighten (decrease) the constant terms of the inequalities based
1500 * on the equalities, without removing any integer points.
1501 * For example, if there is an equality
1502 *
1503 * i = 3 * j
1504 *
1505 * and an inequality
1506 *
1507 * i >= 1
1508 *
1509 * then we want to replace the inequality by
1510 *
1511 * i >= 3
1512 *
1513 * We do this by computing a variable compression and translating
1514 * the constraints to the compressed space.
1515 * If any constraint has coefficients (except the contant term)
1516 * with a common factor "f", then we can replace the constant term "c"
1517 * by
1518 *
1519 * f * floor(c/f)
1520 *
1521 * That is, we add
1522 *
1523 * f * floor(c/f) - c = -fract(c/f)
1524 *
1525 * and we can add the same value to the original constraint.
1526 *
1527 * In the example, the compressed space only contains "j",
1528 * and the inequality translates to
1529 *
1530 * 3 * j - 1 >= 0
1531 *
1532 * We add -fract(-1/3) = -2 to the original constraint to obtain
1533 *
1534 * i - 3 >= 0
1535 */
1536 static struct isl_basic_set *normalize_constraints_in_compressed_space(
1537 struct isl_basic_set *bset)
1538 {
1539 int i;
1540 unsigned total;
1541 struct isl_mat *B, *C;
1542 isl_int gcd;
1543
1544 if (!bset)
1545 return NULL;
1546
1547 if (ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL))
1548 return bset;
1549
1550 if (!bset->n_ineq)
1551 return bset;
1552
1553 bset = isl_basic_set_cow(bset);
1554 if (!bset)
1555 return NULL;
1556
1557 total = isl_basic_set_total_dim(bset);
1558 B = isl_mat_sub_alloc(bset->ctx, bset->eq, 0, bset->n_eq, 0, 1 + total);
1559 C = isl_mat_variable_compression(B, NULL);
1560 if (!C)
1561 return bset;
1562 if (C->n_col == 0) {
1563 isl_mat_free(C);
1564 return isl_basic_set_set_to_empty(bset);
1565 }
1566 B = isl_mat_sub_alloc(bset->ctx, bset->ineq,
1567 0, bset->n_ineq, 0, 1 + total);
1568 C = isl_mat_product(B, C);
1569 if (!C)
1570 return bset;
1571
1572 isl_int_init(gcd);
1573 for (i = 0; i < bset->n_ineq; ++i) {
1574 isl_seq_gcd(C->row[i] + 1, C->n_col - 1, &gcd);
1575 if (isl_int_is_one(gcd))
1576 continue;
1577 isl_int_fdiv_r(C->row[i][0], C->row[i][0], gcd);
1578 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], C->row[i][0]);
1579 }
1580 isl_int_clear(gcd);
1581
1582 isl_mat_free(C);
1583
1584 return bset;
1585 }
1586
1587 /* Remove all information from bset that is redundant in the context
1588 * of context. Both bset and context are assumed to be full-dimensional.
1589 *
1590 * We first * remove the inequalities from "bset"
1591 * that are obviously redundant with respect to some inequality in "context".
1592 *
1593 * If there are any inequalities left, we construct a tableau for
1594 * the context and then add the inequalities of "bset".
1595 * Before adding these inequalities, we freeze all constraints such that
1596 * they won't be considered redundant in terms of the constraints of "bset".
1597 * Then we detect all redundant constraints (among the
1598 * constraints that weren't frozen), first by checking for redundancy in the
1599 * the tableau and then by checking if replacing a constraint by its negation
1600 * would lead to an empty set. This last step is fairly expensive
1601 * and could be optimized by more reuse of the tableau.
1602 * Finally, we update bset according to the results.
1603 */
1604 static __isl_give isl_basic_set *uset_gist_full(__isl_take isl_basic_set *bset,
1605 __isl_take isl_basic_set *context)
1606 {
1607 int i, k;
1608 isl_basic_set *combined = NULL;
1609 struct isl_tab *tab = NULL;
1610 unsigned context_ineq;
1611 unsigned total;
1612
1613 if (!bset || !context)
1614 goto error;
1615
1616 if (isl_basic_set_is_universe(bset)) {
1617 isl_basic_set_free(context);
1618 return bset;
1619 }
1620
1621 if (isl_basic_set_is_universe(context)) {
1622 isl_basic_set_free(context);
1623 return bset;
1624 }
1625
1626 bset = remove_shifted_constraints(bset, context);
1627 if (!bset)
1628 goto error;
1629 if (bset->n_ineq == 0)
1630 goto done;
1631
1632 context_ineq = context->n_ineq;
1633 combined = isl_basic_set_cow(isl_basic_set_copy(context));
1634 combined = isl_basic_set_extend_constraints(combined, 0, bset->n_ineq);
1635 tab = isl_tab_from_basic_set(combined);
1636 for (i = 0; i < context_ineq; ++i)
1637 if (isl_tab_freeze_constraint(tab, i) < 0)
1638 goto error;
1639 tab = isl_tab_extend(tab, bset->n_ineq);
1640 for (i = 0; i < bset->n_ineq; ++i)
1641 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
1642 goto error;
1643 bset = isl_basic_set_add_constraints(combined, bset, 0);
1644 combined = NULL;
1645 if (!bset)
1646 goto error;
1647 if (isl_tab_detect_redundant(tab) < 0)
1648 goto error;
1649 total = isl_basic_set_total_dim(bset);
1650 for (i = context_ineq; i < bset->n_ineq; ++i) {
1651 int is_empty;
1652 if (tab->con[i].is_redundant)
1653 continue;
1654 tab->con[i].is_redundant = 1;
1655 combined = isl_basic_set_dup(bset);
1656 combined = isl_basic_set_update_from_tab(combined, tab);
1657 combined = isl_basic_set_extend_constraints(combined, 0, 1);
1658 k = isl_basic_set_alloc_inequality(combined);
1659 if (k < 0)
1660 goto error;
1661 isl_seq_neg(combined->ineq[k], bset->ineq[i], 1 + total);
1662 isl_int_sub_ui(combined->ineq[k][0], combined->ineq[k][0], 1);
1663 is_empty = isl_basic_set_is_empty(combined);
1664 if (is_empty < 0)
1665 goto error;
1666 isl_basic_set_free(combined);
1667 combined = NULL;
1668 if (!is_empty)
1669 tab->con[i].is_redundant = 0;
1670 }
1671 for (i = 0; i < context_ineq; ++i)
1672 tab->con[i].is_redundant = 1;
1673 bset = isl_basic_set_update_from_tab(bset, tab);
1674 if (bset) {
1675 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1676 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1677 }
1678
1679 isl_tab_free(tab);
1680 done:
1681 bset = isl_basic_set_simplify(bset);
1682 bset = isl_basic_set_finalize(bset);
1683 isl_basic_set_free(context);
1684 return bset;
1685 error:
1686 isl_tab_free(tab);
1687 isl_basic_set_free(combined);
1688 isl_basic_set_free(context);
1689 isl_basic_set_free(bset);
1690 return NULL;
1691 }
1692
1693 /* Remove all information from bset that is redundant in the context
1694 * of context. In particular, equalities that are linear combinations
1695 * of those in context are removed. Then the inequalities that are
1696 * redundant in the context of the equalities and inequalities of
1697 * context are removed.
1698 *
1699 * We first compute the integer affine hull of the intersection,
1700 * compute the gist inside this affine hull and then add back
1701 * those equalities that are not implied by the context.
1702 */
1703 static __isl_give isl_basic_set *uset_gist(__isl_take isl_basic_set *bset,
1704 __isl_take isl_basic_set *context)
1705 {
1706 isl_mat *eq;
1707 isl_mat *T, *T2;
1708 isl_basic_set *aff;
1709 isl_basic_set *aff_context;
1710 unsigned total;
1711
1712 if (!bset || !context)
1713 goto error;
1714
1715 bset = isl_basic_set_intersect(bset, isl_basic_set_copy(context));
1716 if (isl_basic_set_fast_is_empty(bset)) {
1717 isl_basic_set_free(context);
1718 return bset;
1719 }
1720 aff = isl_basic_set_affine_hull(isl_basic_set_copy(bset));
1721 if (!aff)
1722 goto error;
1723 if (isl_basic_set_fast_is_empty(aff)) {
1724 isl_basic_set_free(aff);
1725 isl_basic_set_free(context);
1726 return bset;
1727 }
1728 if (aff->n_eq == 0) {
1729 isl_basic_set_free(aff);
1730 return uset_gist_full(bset, context);
1731 }
1732 total = isl_basic_set_total_dim(bset);
1733 eq = isl_mat_sub_alloc(bset->ctx, aff->eq, 0, aff->n_eq, 0, 1 + total);
1734 eq = isl_mat_cow(eq);
1735 T = isl_mat_variable_compression(eq, &T2);
1736 if (T && T->n_col == 0) {
1737 isl_mat_free(T);
1738 isl_mat_free(T2);
1739 isl_basic_set_free(context);
1740 isl_basic_set_free(aff);
1741 return isl_basic_set_set_to_empty(bset);
1742 }
1743
1744 aff_context = isl_basic_set_affine_hull(isl_basic_set_copy(context));
1745
1746 bset = isl_basic_set_preimage(bset, isl_mat_copy(T));
1747 context = isl_basic_set_preimage(context, T);
1748
1749 bset = uset_gist_full(bset, context);
1750 bset = isl_basic_set_preimage(bset, T2);
1751 bset = isl_basic_set_intersect(bset, aff);
1752 bset = isl_basic_set_reduce_using_equalities(bset, aff_context);
1753
1754 if (bset) {
1755 ISL_F_SET(bset, ISL_BASIC_SET_NO_IMPLICIT);
1756 ISL_F_SET(bset, ISL_BASIC_SET_NO_REDUNDANT);
1757 }
1758
1759 return bset;
1760 error:
1761 isl_basic_set_free(bset);
1762 isl_basic_set_free(context);
1763 return NULL;
1764 }
1765
1766 /* Normalize the divs in "bmap" in the context of the equalities in "context".
1767 * We simply add the equalities in context to bmap and then do a regular
1768 * div normalizations. Better results can be obtained by normalizing
1769 * only the divs in bmap than do not also appear in context.
1770 * We need to be careful to reduce the divs using the equalities
1771 * so that later calls to isl_basic_map_overlying_set wouldn't introduce
1772 * spurious constraints.
1773 */
1774 static struct isl_basic_map *normalize_divs_in_context(
1775 struct isl_basic_map *bmap, struct isl_basic_map *context)
1776 {
1777 int i;
1778 unsigned total_context;
1779 int div_eq;
1780
1781 div_eq = n_pure_div_eq(bmap);
1782 if (div_eq == 0)
1783 return bmap;
1784
1785 if (context->n_div > 0)
1786 bmap = isl_basic_map_align_divs(bmap, context);
1787
1788 total_context = isl_basic_map_total_dim(context);
1789 bmap = isl_basic_map_extend_constraints(bmap, context->n_eq, 0);
1790 for (i = 0; i < context->n_eq; ++i) {
1791 int k;
1792 k = isl_basic_map_alloc_equality(bmap);
1793 isl_seq_cpy(bmap->eq[k], context->eq[i], 1 + total_context);
1794 isl_seq_clr(bmap->eq[k] + 1 + total_context,
1795 isl_basic_map_total_dim(bmap) - total_context);
1796 }
1797 bmap = isl_basic_map_gauss(bmap, NULL);
1798 bmap = normalize_divs(bmap, NULL);
1799 bmap = isl_basic_map_gauss(bmap, NULL);
1800 return bmap;
1801 }
1802
1803 struct isl_basic_map *isl_basic_map_gist(struct isl_basic_map *bmap,
1804 struct isl_basic_map *context)
1805 {
1806 struct isl_basic_set *bset;
1807
1808 if (!bmap || !context)
1809 goto error;
1810
1811 if (isl_basic_map_is_universe(bmap)) {
1812 isl_basic_map_free(context);
1813 return bmap;
1814 }
1815 if (isl_basic_map_fast_is_empty(context)) {
1816 struct isl_dim *dim = isl_dim_copy(bmap->dim);
1817 isl_basic_map_free(context);
1818 isl_basic_map_free(bmap);
1819 return isl_basic_map_universe(dim);
1820 }
1821 if (isl_basic_map_fast_is_empty(bmap)) {
1822 isl_basic_map_free(context);
1823 return bmap;
1824 }
1825
1826 bmap = isl_basic_map_remove_redundancies(bmap);
1827 context = isl_basic_map_remove_redundancies(context);
1828
1829 if (context->n_eq)
1830 bmap = normalize_divs_in_context(bmap, context);
1831
1832 context = isl_basic_map_align_divs(context, bmap);
1833 bmap = isl_basic_map_align_divs(bmap, context);
1834
1835 bset = uset_gist(isl_basic_map_underlying_set(isl_basic_map_copy(bmap)),
1836 isl_basic_map_underlying_set(context));
1837
1838 return isl_basic_map_overlying_set(bset, bmap);
1839 error:
1840 isl_basic_map_free(bmap);
1841 isl_basic_map_free(context);
1842 return NULL;
1843 }
1844
1845 /*
1846 * Assumes context has no implicit divs.
1847 */
1848 __isl_give isl_map *isl_map_gist_basic_map(__isl_take isl_map *map,
1849 __isl_take isl_basic_map *context)
1850 {
1851 int i;
1852
1853 if (!map || !context)
1854 goto error;;
1855
1856 if (isl_basic_map_fast_is_empty(context)) {
1857 struct isl_dim *dim = isl_dim_copy(map->dim);
1858 isl_basic_map_free(context);
1859 isl_map_free(map);
1860 return isl_map_universe(dim);
1861 }
1862
1863 context = isl_basic_map_remove_redundancies(context);
1864 map = isl_map_cow(map);
1865 if (!map || !context)
1866 goto error;;
1867 isl_assert(map->ctx, isl_dim_equal(map->dim, context->dim), goto error);
1868 map = isl_map_compute_divs(map);
1869 for (i = 0; i < map->n; ++i)
1870 context = isl_basic_map_align_divs(context, map->p[i]);
1871 for (i = 0; i < map->n; ++i) {
1872 map->p[i] = isl_basic_map_gist(map->p[i],
1873 isl_basic_map_copy(context));
1874 if (!map->p[i])
1875 goto error;
1876 }
1877 isl_basic_map_free(context);
1878 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
1879 return map;
1880 error:
1881 isl_map_free(map);
1882 isl_basic_map_free(context);
1883 return NULL;
1884 }
1885
1886 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1887 __isl_take isl_map *context)
1888 {
1889 return isl_map_gist_basic_map(map, isl_map_simple_hull(context));
1890 }
1891
1892 struct isl_basic_set *isl_basic_set_gist(struct isl_basic_set *bset,
1893 struct isl_basic_set *context)
1894 {
1895 return (struct isl_basic_set *)isl_basic_map_gist(
1896 (struct isl_basic_map *)bset, (struct isl_basic_map *)context);
1897 }
1898
1899 __isl_give isl_set *isl_set_gist_basic_set(__isl_take isl_set *set,
1900 __isl_take isl_basic_set *context)
1901 {
1902 return (struct isl_set *)isl_map_gist_basic_map((struct isl_map *)set,
1903 (struct isl_basic_map *)context);
1904 }
1905
1906 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1907 __isl_take isl_set *context)
1908 {
1909 return (struct isl_set *)isl_map_gist((struct isl_map *)set,
1910 (struct isl_map *)context);
1911 }
1912
1913 /* Quick check to see if two basic maps are disjoint.
1914 * In particular, we reduce the equalities and inequalities of
1915 * one basic map in the context of the equalities of the other
1916 * basic map and check if we get a contradiction.
1917 */
1918 int isl_basic_map_fast_is_disjoint(struct isl_basic_map *bmap1,
1919 struct isl_basic_map *bmap2)
1920 {
1921 struct isl_vec *v = NULL;
1922 int *elim = NULL;
1923 unsigned total;
1924 int i;
1925
1926 if (!bmap1 || !bmap2)
1927 return -1;
1928 isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
1929 return -1);
1930 if (bmap1->n_div || bmap2->n_div)
1931 return 0;
1932 if (!bmap1->n_eq && !bmap2->n_eq)
1933 return 0;
1934
1935 total = isl_dim_total(bmap1->dim);
1936 if (total == 0)
1937 return 0;
1938 v = isl_vec_alloc(bmap1->ctx, 1 + total);
1939 if (!v)
1940 goto error;
1941 elim = isl_alloc_array(bmap1->ctx, int, total);
1942 if (!elim)
1943 goto error;
1944 compute_elimination_index(bmap1, elim);
1945 for (i = 0; i < bmap2->n_eq; ++i) {
1946 int reduced;
1947 reduced = reduced_using_equalities(v->block.data, bmap2->eq[i],
1948 bmap1, elim);
1949 if (reduced && !isl_int_is_zero(v->block.data[0]) &&
1950 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1951 goto disjoint;
1952 }
1953 for (i = 0; i < bmap2->n_ineq; ++i) {
1954 int reduced;
1955 reduced = reduced_using_equalities(v->block.data,
1956 bmap2->ineq[i], bmap1, elim);
1957 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1958 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1959 goto disjoint;
1960 }
1961 compute_elimination_index(bmap2, elim);
1962 for (i = 0; i < bmap1->n_ineq; ++i) {
1963 int reduced;
1964 reduced = reduced_using_equalities(v->block.data,
1965 bmap1->ineq[i], bmap2, elim);
1966 if (reduced && isl_int_is_neg(v->block.data[0]) &&
1967 isl_seq_first_non_zero(v->block.data + 1, total) == -1)
1968 goto disjoint;
1969 }
1970 isl_vec_free(v);
1971 free(elim);
1972 return 0;
1973 disjoint:
1974 isl_vec_free(v);
1975 free(elim);
1976 return 1;
1977 error:
1978 isl_vec_free(v);
1979 free(elim);
1980 return -1;
1981 }
1982
1983 int isl_basic_set_fast_is_disjoint(struct isl_basic_set *bset1,
1984 struct isl_basic_set *bset2)
1985 {
1986 return isl_basic_map_fast_is_disjoint((struct isl_basic_map *)bset1,
1987 (struct isl_basic_map *)bset2);
1988 }
1989
1990 int isl_map_fast_is_disjoint(struct isl_map *map1, struct isl_map *map2)
1991 {
1992 int i, j;
1993
1994 if (!map1 || !map2)
1995 return -1;
1996
1997 if (isl_map_fast_is_equal(map1, map2))
1998 return 0;
1999
2000 for (i = 0; i < map1->n; ++i) {
2001 for (j = 0; j < map2->n; ++j) {
2002 int d = isl_basic_map_fast_is_disjoint(map1->p[i],
2003 map2->p[j]);
2004 if (d != 1)
2005 return d;
2006 }
2007 }
2008 return 1;
2009 }
2010
2011 int isl_set_fast_is_disjoint(struct isl_set *set1, struct isl_set *set2)
2012 {
2013 return isl_map_fast_is_disjoint((struct isl_map *)set1,
2014 (struct isl_map *)set2);
2015 }
2016
2017 /* Check if we can combine a given div with lower bound l and upper
2018 * bound u with some other div and if so return that other div.
2019 * Otherwise return -1.
2020 *
2021 * We first check that
2022 * - the bounds are opposites of each other (except for the constant
2023 * term)
2024 * - the bounds do not reference any other div
2025 * - no div is defined in terms of this div
2026 *
2027 * Let m be the size of the range allowed on the div by the bounds.
2028 * That is, the bounds are of the form
2029 *
2030 * e <= a <= e + m - 1
2031 *
2032 * with e some expression in the other variables.
2033 * We look for another div b such that no third div is defined in terms
2034 * of this second div b and such that in any constraint that contains
2035 * a (except for the given lower and upper bound), also contains b
2036 * with a coefficient that is m times that of b.
2037 * That is, all constraints (execpt for the lower and upper bound)
2038 * are of the form
2039 *
2040 * e + f (a + m b) >= 0
2041 *
2042 * If so, we return b so that "a + m b" can be replaced by
2043 * a single div "c = a + m b".
2044 */
2045 static int div_find_coalesce(struct isl_basic_map *bmap, int *pairs,
2046 unsigned div, unsigned l, unsigned u)
2047 {
2048 int i, j;
2049 unsigned dim;
2050 int coalesce = -1;
2051
2052 if (bmap->n_div <= 1)
2053 return -1;
2054 dim = isl_dim_total(bmap->dim);
2055 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim, div) != -1)
2056 return -1;
2057 if (isl_seq_first_non_zero(bmap->ineq[l] + 1 + dim + div + 1,
2058 bmap->n_div - div - 1) != -1)
2059 return -1;
2060 if (!isl_seq_is_neg(bmap->ineq[l] + 1, bmap->ineq[u] + 1,
2061 dim + bmap->n_div))
2062 return -1;
2063
2064 for (i = 0; i < bmap->n_div; ++i) {
2065 if (isl_int_is_zero(bmap->div[i][0]))
2066 continue;
2067 if (!isl_int_is_zero(bmap->div[i][1 + 1 + dim + div]))
2068 return -1;
2069 }
2070
2071 isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2072 if (isl_int_is_neg(bmap->ineq[l][0])) {
2073 isl_int_sub(bmap->ineq[l][0],
2074 bmap->ineq[l][0], bmap->ineq[u][0]);
2075 bmap = isl_basic_map_copy(bmap);
2076 bmap = isl_basic_map_set_to_empty(bmap);
2077 isl_basic_map_free(bmap);
2078 return -1;
2079 }
2080 isl_int_add_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2081 for (i = 0; i < bmap->n_div; ++i) {
2082 if (i == div)
2083 continue;
2084 if (!pairs[i])
2085 continue;
2086 for (j = 0; j < bmap->n_div; ++j) {
2087 if (isl_int_is_zero(bmap->div[j][0]))
2088 continue;
2089 if (!isl_int_is_zero(bmap->div[j][1 + 1 + dim + i]))
2090 break;
2091 }
2092 if (j < bmap->n_div)
2093 continue;
2094 for (j = 0; j < bmap->n_ineq; ++j) {
2095 int valid;
2096 if (j == l || j == u)
2097 continue;
2098 if (isl_int_is_zero(bmap->ineq[j][1 + dim + div]))
2099 continue;
2100 if (isl_int_is_zero(bmap->ineq[j][1 + dim + i]))
2101 break;
2102 isl_int_mul(bmap->ineq[j][1 + dim + div],
2103 bmap->ineq[j][1 + dim + div],
2104 bmap->ineq[l][0]);
2105 valid = isl_int_eq(bmap->ineq[j][1 + dim + div],
2106 bmap->ineq[j][1 + dim + i]);
2107 isl_int_divexact(bmap->ineq[j][1 + dim + div],
2108 bmap->ineq[j][1 + dim + div],
2109 bmap->ineq[l][0]);
2110 if (!valid)
2111 break;
2112 }
2113 if (j < bmap->n_ineq)
2114 continue;
2115 coalesce = i;
2116 break;
2117 }
2118 isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
2119 isl_int_sub(bmap->ineq[l][0], bmap->ineq[l][0], bmap->ineq[u][0]);
2120 return coalesce;
2121 }
2122
2123 /* Given a lower and an upper bound on div i, construct an inequality
2124 * that when nonnegative ensures that this pair of bounds always allows
2125 * for an integer value of the given div.
2126 * The lower bound is inequality l, while the upper bound is inequality u.
2127 * The constructed inequality is stored in ineq.
2128 * g, fl, fu are temporary scalars.
2129 *
2130 * Let the upper bound be
2131 *
2132 * -n_u a + e_u >= 0
2133 *
2134 * and the lower bound
2135 *
2136 * n_l a + e_l >= 0
2137 *
2138 * Let n_u = f_u g and n_l = f_l g, with g = gcd(n_u, n_l).
2139 * We have
2140 *
2141 * - f_u e_l <= f_u f_l g a <= f_l e_u
2142 *
2143 * Since all variables are integer valued, this is equivalent to
2144 *
2145 * - f_u e_l - (f_u - 1) <= f_u f_l g a <= f_l e_u + (f_l - 1)
2146 *
2147 * If this interval is at least f_u f_l g, then it contains at least
2148 * one integer value for a.
2149 * That is, the test constraint is
2150 *
2151 * f_l e_u + f_u e_l + f_l - 1 + f_u - 1 + 1 >= f_u f_l g
2152 */
2153 static void construct_test_ineq(struct isl_basic_map *bmap, int i,
2154 int l, int u, isl_int *ineq, isl_int g, isl_int fl, isl_int fu)
2155 {
2156 unsigned dim;
2157 dim = isl_dim_total(bmap->dim);
2158
2159 isl_int_gcd(g, bmap->ineq[l][1 + dim + i], bmap->ineq[u][1 + dim + i]);
2160 isl_int_divexact(fl, bmap->ineq[l][1 + dim + i], g);
2161 isl_int_divexact(fu, bmap->ineq[u][1 + dim + i], g);
2162 isl_int_neg(fu, fu);
2163 isl_seq_combine(ineq, fl, bmap->ineq[u], fu, bmap->ineq[l],
2164 1 + dim + bmap->n_div);
2165 isl_int_add(ineq[0], ineq[0], fl);
2166 isl_int_add(ineq[0], ineq[0], fu);
2167 isl_int_sub_ui(ineq[0], ineq[0], 1);
2168 isl_int_mul(g, g, fl);
2169 isl_int_mul(g, g, fu);
2170 isl_int_sub(ineq[0], ineq[0], g);
2171 }
2172
2173 /* Remove more kinds of divs that are not strictly needed.
2174 * In particular, if all pairs of lower and upper bounds on a div
2175 * are such that they allow at least one integer value of the div,
2176 * the we can eliminate the div using Fourier-Motzkin without
2177 * introducing any spurious solutions.
2178 */
2179 static struct isl_basic_map *drop_more_redundant_divs(
2180 struct isl_basic_map *bmap, int *pairs, int n)
2181 {
2182 struct isl_tab *tab = NULL;
2183 struct isl_vec *vec = NULL;
2184 unsigned dim;
2185 int remove = -1;
2186 isl_int g, fl, fu;
2187
2188 isl_int_init(g);
2189 isl_int_init(fl);
2190 isl_int_init(fu);
2191
2192 if (!bmap)
2193 goto error;
2194
2195 dim = isl_dim_total(bmap->dim);
2196 vec = isl_vec_alloc(bmap->ctx, 1 + dim + bmap->n_div);
2197 if (!vec)
2198 goto error;
2199
2200 tab = isl_tab_from_basic_map(bmap);
2201
2202 while (n > 0) {
2203 int i, l, u;
2204 int best = -1;
2205 enum isl_lp_result res;
2206
2207 for (i = 0; i < bmap->n_div; ++i) {
2208 if (!pairs[i])
2209 continue;
2210 if (best >= 0 && pairs[best] <= pairs[i])
2211 continue;
2212 best = i;
2213 }
2214
2215 i = best;
2216 for (l = 0; l < bmap->n_ineq; ++l) {
2217 if (!isl_int_is_pos(bmap->ineq[l][1 + dim + i]))
2218 continue;
2219 for (u = 0; u < bmap->n_ineq; ++u) {
2220 if (!isl_int_is_neg(bmap->ineq[u][1 + dim + i]))
2221 continue;
2222 construct_test_ineq(bmap, i, l, u,
2223 vec->el, g, fl, fu);
2224 res = isl_tab_min(tab, vec->el,
2225 bmap->ctx->one, &g, NULL, 0);
2226 if (res == isl_lp_error)
2227 goto error;
2228 if (res == isl_lp_empty) {
2229 bmap = isl_basic_map_set_to_empty(bmap);
2230 break;
2231 }
2232 if (res != isl_lp_ok || isl_int_is_neg(g))
2233 break;
2234 }
2235 if (u < bmap->n_ineq)
2236 break;
2237 }
2238 if (l == bmap->n_ineq) {
2239 remove = i;
2240 break;
2241 }
2242 pairs[i] = 0;
2243 --n;
2244 }
2245
2246 isl_tab_free(tab);
2247 isl_vec_free(vec);
2248
2249 isl_int_clear(g);
2250 isl_int_clear(fl);
2251 isl_int_clear(fu);
2252
2253 free(pairs);
2254
2255 if (remove < 0)
2256 return bmap;
2257
2258 bmap = isl_basic_map_remove(bmap, isl_dim_div, remove, 1);
2259 return isl_basic_map_drop_redundant_divs(bmap);
2260 error:
2261 free(pairs);
2262 isl_basic_map_free(bmap);
2263 isl_tab_free(tab);
2264 isl_vec_free(vec);
2265 isl_int_clear(g);
2266 isl_int_clear(fl);
2267 isl_int_clear(fu);
2268 return NULL;
2269 }
2270
2271 /* Given a pair of divs div1 and div2 such that, expect for the lower bound l
2272 * and the upper bound u, div1 always occurs together with div2 in the form
2273 * (div1 + m div2), where m is the constant range on the variable div1
2274 * allowed by l and u, replace the pair div1 and div2 by a single
2275 * div that is equal to div1 + m div2.
2276 *
2277 * The new div will appear in the location that contains div2.
2278 * We need to modify all constraints that contain
2279 * div2 = (div - div1) / m
2280 * (If a constraint does not contain div2, it will also not contain div1.)
2281 * If the constraint also contains div1, then we know they appear
2282 * as f (div1 + m div2) and we can simply replace (div1 + m div2) by div,
2283 * i.e., the coefficient of div is f.
2284 *
2285 * Otherwise, we first need to introduce div1 into the constraint.
2286 * Let the l be
2287 *
2288 * div1 + f >=0
2289 *
2290 * and u
2291 *
2292 * -div1 + f' >= 0
2293 *
2294 * A lower bound on div2
2295 *
2296 * n div2 + t >= 0
2297 *
2298 * can be replaced by
2299 *
2300 * (n * (m div 2 + div1) + m t + n f)/g >= 0
2301 *
2302 * with g = gcd(m,n).
2303 * An upper bound
2304 *
2305 * -n div2 + t >= 0
2306 *
2307 * can be replaced by
2308 *
2309 * (-n * (m div2 + div1) + m t + n f')/g >= 0
2310 *
2311 * These constraint are those that we would obtain from eliminating
2312 * div1 using Fourier-Motzkin.
2313 *
2314 * After all constraints have been modified, we drop the lower and upper
2315 * bound and then drop div1.
2316 */
2317 static struct isl_basic_map *coalesce_divs(struct isl_basic_map *bmap,
2318 unsigned div1, unsigned div2, unsigned l, unsigned u)
2319 {
2320 isl_int a;
2321 isl_int b;
2322 isl_int m;
2323 unsigned dim, total;
2324 int i;
2325
2326 dim = isl_dim_total(bmap->dim);
2327 total = 1 + dim + bmap->n_div;
2328
2329 isl_int_init(a);
2330 isl_int_init(b);
2331 isl_int_init(m);
2332 isl_int_add(m, bmap->ineq[l][0], bmap->ineq[u][0]);
2333 isl_int_add_ui(m, m, 1);
2334
2335 for (i = 0; i < bmap->n_ineq; ++i) {
2336 if (i == l || i == u)
2337 continue;
2338 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div2]))
2339 continue;
2340 if (isl_int_is_zero(bmap->ineq[i][1 + dim + div1])) {
2341 isl_int_gcd(b, m, bmap->ineq[i][1 + dim + div2]);
2342 isl_int_divexact(a, m, b);
2343 isl_int_divexact(b, bmap->ineq[i][1 + dim + div2], b);
2344 if (isl_int_is_pos(b)) {
2345 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2346 b, bmap->ineq[l], total);
2347 } else {
2348 isl_int_neg(b, b);
2349 isl_seq_combine(bmap->ineq[i], a, bmap->ineq[i],
2350 b, bmap->ineq[u], total);
2351 }
2352 }
2353 isl_int_set(bmap->ineq[i][1 + dim + div2],
2354 bmap->ineq[i][1 + dim + div1]);
2355 isl_int_set_si(bmap->ineq[i][1 + dim + div1], 0);
2356 }
2357
2358 isl_int_clear(a);
2359 isl_int_clear(b);
2360 isl_int_clear(m);
2361 if (l > u) {
2362 isl_basic_map_drop_inequality(bmap, l);
2363 isl_basic_map_drop_inequality(bmap, u);
2364 } else {
2365 isl_basic_map_drop_inequality(bmap, u);
2366 isl_basic_map_drop_inequality(bmap, l);
2367 }
2368 bmap = isl_basic_map_drop_div(bmap, div1);
2369 return bmap;
2370 }
2371
2372 /* First check if we can coalesce any pair of divs and
2373 * then continue with dropping more redundant divs.
2374 *
2375 * We loop over all pairs of lower and upper bounds on a div
2376 * with coefficient 1 and -1, respectively, check if there
2377 * is any other div "c" with which we can coalesce the div
2378 * and if so, perform the coalescing.
2379 */
2380 static struct isl_basic_map *coalesce_or_drop_more_redundant_divs(
2381 struct isl_basic_map *bmap, int *pairs, int n)
2382 {
2383 int i, l, u;
2384 unsigned dim;
2385
2386 dim = isl_dim_total(bmap->dim);
2387
2388 for (i = 0; i < bmap->n_div; ++i) {
2389 if (!pairs[i])
2390 continue;
2391 for (l = 0; l < bmap->n_ineq; ++l) {
2392 if (!isl_int_is_one(bmap->ineq[l][1 + dim + i]))
2393 continue;
2394 for (u = 0; u < bmap->n_ineq; ++u) {
2395 int c;
2396
2397 if (!isl_int_is_negone(bmap->ineq[u][1+dim+i]))
2398 continue;
2399 c = div_find_coalesce(bmap, pairs, i, l, u);
2400 if (c < 0)
2401 continue;
2402 free(pairs);
2403 bmap = coalesce_divs(bmap, i, c, l, u);
2404 return isl_basic_map_drop_redundant_divs(bmap);
2405 }
2406 }
2407 }
2408
2409 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
2410 return bmap;
2411
2412 return drop_more_redundant_divs(bmap, pairs, n);
2413 }
2414
2415 /* Remove divs that are not strictly needed.
2416 * In particular, if a div only occurs positively (or negatively)
2417 * in constraints, then it can simply be dropped.
2418 * Also, if a div occurs only occurs in two constraints and if moreover
2419 * those two constraints are opposite to each other, except for the constant
2420 * term and if the sum of the constant terms is such that for any value
2421 * of the other values, there is always at least one integer value of the
2422 * div, i.e., if one plus this sum is greater than or equal to
2423 * the (absolute value) of the coefficent of the div in the constraints,
2424 * then we can also simply drop the div.
2425 *
2426 * If any divs are left after these simple checks then we move on
2427 * to more complicated cases in drop_more_redundant_divs.
2428 */
2429 struct isl_basic_map *isl_basic_map_drop_redundant_divs(
2430 struct isl_basic_map *bmap)
2431 {
2432 int i, j;
2433 unsigned off;
2434 int *pairs = NULL;
2435 int n = 0;
2436
2437 if (!bmap)
2438 goto error;
2439
2440 off = isl_dim_total(bmap->dim);
2441 pairs = isl_calloc_array(bmap->ctx, int, bmap->n_div);
2442 if (!pairs)
2443 goto error;
2444
2445 for (i = 0; i < bmap->n_div; ++i) {
2446 int pos, neg;
2447 int last_pos, last_neg;
2448 int redundant;
2449 int defined;
2450
2451 defined = !isl_int_is_zero(bmap->div[i][0]);
2452 for (j = 0; j < bmap->n_eq; ++j)
2453 if (!isl_int_is_zero(bmap->eq[j][1 + off + i]))
2454 break;
2455 if (j < bmap->n_eq)
2456 continue;
2457 ++n;
2458 pos = neg = 0;
2459 for (j = 0; j < bmap->n_ineq; ++j) {
2460 if (isl_int_is_pos(bmap->ineq[j][1 + off + i])) {
2461 last_pos = j;
2462 ++pos;
2463 }
2464 if (isl_int_is_neg(bmap->ineq[j][1 + off + i])) {
2465 last_neg = j;
2466 ++neg;
2467 }
2468 }
2469 pairs[i] = pos * neg;
2470 if (pairs[i] == 0) {
2471 for (j = bmap->n_ineq - 1; j >= 0; --j)
2472 if (!isl_int_is_zero(bmap->ineq[j][1+off+i]))
2473 isl_basic_map_drop_inequality(bmap, j);
2474 bmap = isl_basic_map_drop_div(bmap, i);
2475 free(pairs);
2476 return isl_basic_map_drop_redundant_divs(bmap);
2477 }
2478 if (pairs[i] != 1)
2479 continue;
2480 if (!isl_seq_is_neg(bmap->ineq[last_pos] + 1,
2481 bmap->ineq[last_neg] + 1,
2482 off + bmap->n_div))
2483 continue;
2484
2485 isl_int_add(bmap->ineq[last_pos][0],
2486 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2487 isl_int_add_ui(bmap->ineq[last_pos][0],
2488 bmap->ineq[last_pos][0], 1);
2489 redundant = isl_int_ge(bmap->ineq[last_pos][0],
2490 bmap->ineq[last_pos][1+off+i]);
2491 isl_int_sub_ui(bmap->ineq[last_pos][0],
2492 bmap->ineq[last_pos][0], 1);
2493 isl_int_sub(bmap->ineq[last_pos][0],
2494 bmap->ineq[last_pos][0], bmap->ineq[last_neg][0]);
2495 if (!redundant) {
2496 if (defined ||
2497 !ok_to_set_div_from_bound(bmap, i, last_pos)) {
2498 pairs[i] = 0;
2499 --n;
2500 continue;
2501 }
2502 bmap = set_div_from_lower_bound(bmap, i, last_pos);
2503 bmap = isl_basic_map_simplify(bmap);
2504 free(pairs);
2505 return isl_basic_map_drop_redundant_divs(bmap);
2506 }
2507 if (last_pos > last_neg) {
2508 isl_basic_map_drop_inequality(bmap, last_pos);
2509 isl_basic_map_drop_inequality(bmap, last_neg);
2510 } else {
2511 isl_basic_map_drop_inequality(bmap, last_neg);
2512 isl_basic_map_drop_inequality(bmap, last_pos);
2513 }
2514 bmap = isl_basic_map_drop_div(bmap, i);
2515 free(pairs);
2516 return isl_basic_map_drop_redundant_divs(bmap);
2517 }
2518
2519 if (n > 0)
2520 return coalesce_or_drop_more_redundant_divs(bmap, pairs, n);
2521
2522 free(pairs);
2523 return bmap;
2524 error:
2525 free(pairs);
2526 isl_basic_map_free(bmap);
2527 return NULL;
2528 }
2529
2530 struct isl_basic_set *isl_basic_set_drop_redundant_divs(
2531 struct isl_basic_set *bset)
2532 {
2533 return (struct isl_basic_set *)
2534 isl_basic_map_drop_redundant_divs((struct isl_basic_map *)bset);
2535 }
2536
2537 struct isl_map *isl_map_drop_redundant_divs(struct isl_map *map)
2538 {
2539 int i;
2540
2541 if (!map)
2542 return NULL;
2543 for (i = 0; i < map->n; ++i) {
2544 map->p[i] = isl_basic_map_drop_redundant_divs(map->p[i]);
2545 if (!map->p[i])
2546 goto error;
2547 }
2548 ISL_F_CLR(map, ISL_MAP_NORMALIZED);
2549 return map;
2550 error:
2551 isl_map_free(map);
2552 return NULL;
2553 }
2554
2555 struct isl_set *isl_set_drop_redundant_divs(struct isl_set *set)
2556 {
2557 return (struct isl_set *)
2558 isl_map_drop_redundant_divs((struct isl_map *)set);
2559 }
Integer set library